Properties

Label 12.5.d
Level 12
Weight 5
Character orbit d
Rep. character \(\chi_{12}(7,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(12, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\( 4q + 6q^{2} - 20q^{4} + 24q^{5} - 18q^{6} - 108q^{9} + O(q^{10}) \) \( 4q + 6q^{2} - 20q^{4} + 24q^{5} - 18q^{6} - 108q^{9} - 172q^{10} + 180q^{12} + 296q^{13} + 600q^{14} + 112q^{16} - 600q^{17} - 162q^{18} - 1368q^{20} - 144q^{21} - 1128q^{22} + 1296q^{24} + 972q^{25} + 1692q^{26} + 1488q^{28} + 888q^{29} - 1980q^{30} - 2784q^{32} + 720q^{33} - 484q^{34} + 540q^{36} - 4408q^{37} + 4680q^{38} + 1664q^{40} + 552q^{41} - 2088q^{42} - 3696q^{44} - 648q^{45} - 384q^{46} + 1008q^{48} - 572q^{49} - 1038q^{50} + 6008q^{52} + 5112q^{53} + 486q^{54} + 1728q^{56} + 5616q^{57} - 124q^{58} - 2664q^{60} + 4232q^{61} - 7224q^{62} - 14720q^{64} - 18192q^{65} + 4824q^{66} + 5496q^{68} - 9792q^{69} + 6096q^{70} + 8840q^{73} - 4116q^{74} - 1872q^{76} + 20928q^{77} + 9900q^{78} + 25632q^{80} + 2916q^{81} + 3740q^{82} - 10512q^{84} - 10256q^{85} - 19560q^{86} - 8640q^{88} - 25080q^{89} + 4644q^{90} + 18816q^{92} - 17136q^{93} - 5232q^{94} - 8352q^{96} + 23048q^{97} - 5850q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.5.d.a \(4\) \(1.240\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(6\) \(0\) \(24\) \(0\) \(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 6 T + 28 T^{2} - 96 T^{3} + 256 T^{4} \)
$3$ \( ( 1 + 27 T^{2} )^{2} \)
$5$ \( ( 1 - 12 T + 454 T^{2} - 7500 T^{3} + 390625 T^{4} )^{2} \)
$7$ \( 1 - 4516 T^{2} + 16148934 T^{4} - 26033841316 T^{6} + 33232930569601 T^{8} \)
$11$ \( 1 - 36196 T^{2} + 708332166 T^{4} - 7758934056676 T^{6} + 45949729863572161 T^{8} \)
$13$ \( ( 1 - 148 T + 32646 T^{2} - 4227028 T^{3} + 815730721 T^{4} )^{2} \)
$17$ \( ( 1 + 300 T + 186214 T^{2} + 25056300 T^{3} + 6975757441 T^{4} )^{2} \)
$19$ \( 1 - 195556 T^{2} + 17286835974 T^{4} - 3321237654045796 T^{6} + \)\(28\!\cdots\!81\)\( T^{8} \)
$23$ \( 1 - 655492 T^{2} + 255175536006 T^{4} - 51332224363813252 T^{6} + \)\(61\!\cdots\!61\)\( T^{8} \)
$29$ \( ( 1 - 444 T + 1423078 T^{2} - 314032764 T^{3} + 500246412961 T^{4} )^{2} \)
$31$ \( 1 - 2090020 T^{2} + 2465294161734 T^{4} - 1782559326072438820 T^{6} + \)\(72\!\cdots\!81\)\( T^{8} \)
$37$ \( ( 1 + 2204 T + 4842918 T^{2} + 4130650844 T^{3} + 3512479453921 T^{4} )^{2} \)
$41$ \( ( 1 - 276 T + 5507494 T^{2} - 779910036 T^{3} + 7984925229121 T^{4} )^{2} \)
$43$ \( 1 - 3593572 T^{2} + 5893643026566 T^{4} - 42002389247979180772 T^{6} + \)\(13\!\cdots\!01\)\( T^{8} \)
$47$ \( 1 - 16853380 T^{2} + 118578854811654 T^{4} - \)\(40\!\cdots\!80\)\( T^{6} + \)\(56\!\cdots\!21\)\( T^{8} \)
$53$ \( ( 1 - 2556 T + 17173798 T^{2} - 20168069436 T^{3} + 62259690411361 T^{4} )^{2} \)
$59$ \( 1 - 32722276 T^{2} + 559903452302214 T^{4} - \)\(48\!\cdots\!96\)\( T^{6} + \)\(21\!\cdots\!41\)\( T^{8} \)
$61$ \( ( 1 - 2116 T + 16830246 T^{2} - 29297799556 T^{3} + 191707312997281 T^{4} )^{2} \)
$67$ \( 1 - 53256676 T^{2} + 1338152481850374 T^{4} - \)\(21\!\cdots\!16\)\( T^{6} + \)\(16\!\cdots\!81\)\( T^{8} \)
$71$ \( 1 - 79127428 T^{2} + 2740885222137990 T^{4} - \)\(51\!\cdots\!08\)\( T^{6} + \)\(41\!\cdots\!21\)\( T^{8} \)
$73$ \( ( 1 - 4420 T + 3693510 T^{2} - 125520225220 T^{3} + 806460091894081 T^{4} )^{2} \)
$79$ \( 1 - 86136100 T^{2} + 4459690111983174 T^{4} - \)\(13\!\cdots\!00\)\( T^{6} + \)\(23\!\cdots\!21\)\( T^{8} \)
$83$ \( 1 - 855268 T^{2} + 4298268871421190 T^{4} - \)\(19\!\cdots\!88\)\( T^{6} + \)\(50\!\cdots\!81\)\( T^{8} \)
$89$ \( ( 1 + 12540 T + 132835270 T^{2} + 786787702140 T^{3} + 3936588805702081 T^{4} )^{2} \)
$97$ \( ( 1 - 11524 T + 146880774 T^{2} - 1020211434244 T^{3} + 7837433594376961 T^{4} )^{2} \)
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